A150338 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 1), (0, 0, -1), (0, 0, 1), (1, 0, 1)}.

1, 2, 7, 23, 86, 324, 1299, 5248, 21775, 91053, 386100, 1650934, 7124220, 30968386, 135455089, 595865245, 2633401172, 11691086039, 52101621996, 233046312802, 1045751149946, 4706689810491, 21241503177894, 96104232133673, 435826985828029, 1980691355824627, 9019785417646572, 41151396449899485

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A179533 A352173 A150337 * A150339 A150340 A339038

Adjacent sequences: A150335 A150336 A150337 * A150339 A150340 A150341

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved